We interpret multi-product supply chains (SCs) as coordinated markets, casting SC optimization problems market clearing that allocate resources to stakeholders and determine prices. The interpretation allows us establish fundamental properties explain how physical (primal variables) associated economic values (dual flow in SCs. use duality theory why incentivizing markets by forcing stakeholder...

In this paper, for the first time, notion of multi complex numbers and number valued inner product is introduced in linear (vector) space. Starting from definition, some basic properties spaces are studied along with examples. Multi parallelogram law polarization identity established

Here, we consider single vendor-buyer model with multi-product and multi-customer and multi-facility location-production-distribution problem. It is assumed that the players of the supply chain are coordinated by sharing information. Vendor manufactures produce different products at different plants with limited capacities and then distribute the products to the consumers according to determini...

The theory of constraints is an approach to production planning and control that emphasizes on the constraints to increase throughput by effectively managing constraint resources. One application in theory of constraints is product mix decision. Product mix influences the performance measures in multi-product manufacturing system. This paper presents an alternative approach by using of goal pro...

Recently, scholars and practitioners have shown an increased interest in the field of sustainable supplier selection and order lot-sizing. While several studies have recently carried out on this field, far too little attention has been given to formulating a multi-objective model for the integrated problem of multi-period multi-product order lot-sizing and sustainable supplier selection under i...

Many multi-product firms incur a complexity fixed cost when offering different product lines in different quality tiers relative to the case when offering all products lines in the same quality tier (high or low). Such fixed costs create an interdependency between firms’choices of quality tiers across different product lines, even when demands are independent. We investigate the effects of this...

Software constitutes a major cost factor when developing technical systems. To reduce this cost, systematic reuse of assets is necessary from early on when developing similar products—an approach that has become known as software product line engineering. The automation of product derivation, that is, the automated product creation from core assets, is one of the success factors of product line...

product mix problem (pmp) is one of the most important and complicated problems in production systems. different approaches have been applied to solve this problem, among them, theory of constraints (toc) has been widely considered since 1990s. this paper develops a distinguished algorithm to solve product mix prob-lems that is efficient both in single and multi-bottleneck problems. at first, t...

this paper proposes a new mathematical model for the integrated procurement-production-distribution problem of a fuzzy mixed integer linear programming (fmilp) type. considering the uncertainty in real problems, a number of parameters such as demand, capacity, and cost where their values are not available or known precisely, have been considered as trapezoidal fuzzy numbers. to solve fuzzy mixe...